Question: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x+4y &= 7 \\ x-6y &= -7\end{align*}$
Answer: Begin by moving the $y$ -term in the second equation to the right side of the equation. $x = {6y-7}$ Substitute this expression for $x$ in the first equation. $4({6y - 7}) + 4y = 7$ $24y - 28 + 4y = 7$ Simplify by combining terms, then solve for $y$ $28y - 28 = 7$ $28y = 35$ $y = \dfrac{5}{4}$ Substitute $\dfrac{5}{4}$ for $y$ in the top equation. $4x+4( \dfrac{5}{4}) = 7$ $4x+5 = 7$ $4x = 2$ $x = \dfrac{1}{2}$ The solution is $\enspace x = \dfrac{1}{2}, \enspace y = \dfrac{5}{4}$.